Is there a Hebb neural network?
In machine learning, the idea behind Hebbian learning is to strengthen (or weaken) the connection (the weight) between the neurons that have similar (or, respectively, dissimilar) outputs, where "similar" can be defined in different ways (e.g. it could be based on the sign of the output of the neurons). 

Hebbian learning is a more biologically plausible way of learning than back-propagation, because it is a "local learning strategy" (you locally update the connections and not all the connections of the model at the same time), as opposed to back-propagation, which is a "global learning strategy" (where all connections are usually updated at once, given a "global error" of the network).

There are several neural networks (or models) that can learn in a Hebbian fashion: for example, the Hopfield network or Numenta's temporal memory.